Applications of conformal field theory and string theory in statistical systems

This thesis investigates different aspects of conformal field theory and string theory and their applications in statistical properties of systems. First, we study the free fermions in planar Ising model and its scaling limit at criticality. On the one hand, we examine the relation between the transfer matrix formalism and discrete holomorphicity. We show that the fermion operators of the Ising model satisfy a complexification of the defining relations of s-holomorphicity, a strong notion of discrete holomorphicity, and examples of fermion correlation functions are shown to reproduce s-holomorphic parafermionic observables. On the other hand, we study the relation between fermionic conformal field theory and Schramm Loewner evolution by focusing on the interfaces and fermionic correlation functions of the Ising model. We demonstrate an explicit, rigorous realization of the CFT/SLE correspondence in the case of Ising model. Second, we develop a statistical framework for bosonic string theory in order to study transport properties of black holes in the context of membrane paradigm. We find that the shear viscosity of a highly excited bosonic string is equal to that of black hole horizon up to a numerical factor.

Grantor dc:publisher

Helsingin yliopisto

Year dc:date.issued

2013

Author dc:creator

• Zahabi, Seyedali

• mathematical physics

Statement dc:rights

• Julkaisu on tekijänoikeussäännösten alainen. Teosta voi lukea ja tulostaa henkilökohtaista käyttöä varten. Käyttö kaupallisiin tarkoituksiin on kielletty.
• This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.
• Publikationen är skyddad av upphovsrätten. Den får läsas och skrivas ut för personligt bruk. Användning i kommersiellt syfte är förbjuden.

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/10138/40728

OAI record oai:identifier

https://helda.helsinki.fi/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Ahelda.helsinki.fi%3A10138%2F40728